There seems to be a "city pass" for Barcelona as well as the "Barcelona Card". I assume it is the "city pass" you are considering.
Much of the value of this pass lies in the hop-on/hop-off bus. If you would not otherwise spend the money on the HO/HO bus, the city-pass will probably not be cost-effective for you. I am not a fan of HO/HOs in general, and I observed an incredibly long line of people waiting to board the next HO/HO (not yet present) at Placa Catalunya in August 2016. I don't think HO/HOs are an efficient means of transportation in most places. Barcelona has a very good subway that is quite inexpensive, especially if you buy a T-10 ticket (which can be shared by multiple members of your group if desired). Short bus tours for the purpose of orientation are probably cheaper than the HO/HO bus.
One of the two included attractions is La Sagrada Familia. There is no mention of ascending a tower, which some visitors like to do. As far as I know, there is no way to buy a separate ticket for the tower; you must buy a combo ticket that includes entry to the church plus access to the tower. Therefore, I think if you have the city-pass and want to go up one of the towers, you'll have to pay again for the full LSF ticket.
I wouldn't expect there to be a problem with getting good days and time slots if you purchased the pass soon, but LSF has limited capacity for each time block, and Parc Guell is switching to that model sometime in 2019. Buying the city-pass shortly before your trip would be risky, because the time slots you need might be sold out.
Only you can determine whether you will, might, or definitely will not save money with the city-pass, because only you know how many of the 20%-off sights you want to see and how many you'll be able to squeeze in. If you are flying to Barcelona from the US or Canada, you may be brain-dead on March 22 and have less than 3 full days for city sightseeing.
Furthermore, I see no assurance that you can use the card to obtain the discount on tickets purchased online in advance. That's really the only manageable way to see the Picasso Museum, Casa Mila or Casa Batllo. If you just show up with a city-pass to buy a ticket to those attractions on the spot, you will probably wait in an extremely long line and find out that either all the day's tickets have been sold or the available tickets are for many hours later. The Camp Nou Experience (soccer) sells out very early and would almost certainly not be available at all if you tried to buy tickets on the spot.
I looked at the Casa Mila web site and found a 3-euro discount for online purchases (22 euros rather than 25 euros). The 20% discount for in-person purchases is only 5 euros (20 euros rather than 25 euros), so the difference is far less than 20% and appears to require you to wait until you arrive in Barcelona to obtain the discounted tickets, wasting precious vacation time in line--and possibly finding the sight sold out for the period of your visit.
Casa Batllo has a 4-euro discount for online purchases.
Both Casa Mila and Casa Batllo have senior discounts (5.50 euros and 3 euros, respectively). I have no idea whether the 20% city-pass discount can be applied to the senior entry rates--not that it really matters, since I'm sure you're not interested in standing in lines at the ticket windows anyway. The senior-discount tickets can be purchased in advance on line (if you are age-qualified).
You can enjoy the modernista exteriors of many lovely buildings without paying any entry fees. I believe the least expensive significant modernista sight is the Sant Pau complex, which is 14 euros (17 euros with the audio guide). It is a lovely, multi-building complex with very pretty grounds. A bargain by Barcelona standards.
The Picasso Museum is often a miserable experience because of severe crowding. It is worth the money only for folks really interested in early Picasso.